Commensurability of automorphism groups

Abstract

We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra heuristics on class groups. The number theoretic implications will be addressed in a separate paper.

26 pages; improved the introduction and the exposition in the body of the paper. The final version is to appear in Compositio Math

Cited by in corpus (5)

• On class groups of random number fields
• Moments and interpretations of the Cohen-Lenstra-Martinet heuristics
• Finitely generated abelian groups of units
• Characters of the group ${\mathrm{EL}}_d(R)$ for a commutative Noetherian ring $R$
• The analytic class number formula for $1$-dimensional affine schemes